LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – PHYSICS
FOURTH SEMESTER – APRIL 2012
MT 4203/4200 - ADVANCED MATHEMATICS FOR PHYSICS
Date : 19-04-2012
Time : 1:00 - 4:00
Dept. No.
Max. : 100 Marks
SECTION – A
ANSWER ALL QUESTIONS:
1. Evaluate
2.
3.
4.
5.
6.
(10 x 2 = 20)
Define Fourier series.
State the necessary and sufficient condition for the ordinary differential equation to be exact.
Write the general solution when the roots are imaginary.
Define Beta function.
State the relation between Beta and Gamma function.
7. If the vector f  3xi   x  y  j  azk
is solenoidal, find .
8. State Stokes theorem
9. Define any two properties of cyclic group.
10. Define Kronecker’s delta.
SECTION – B
ANSWER ANY FIVE QUESTIONS:
(5 x 8 = 40)
11. Solve
.
12. Find a sine series for
in the range
13. Evaluate
to .
.
14. Solve
.
15. Solve
.
16. Evaluate
, where R is the region in the first quadrant bounded by the hyperbolas
and
and the circles
and
.
17. If
, find
and
at
.
18. Prove that the set
is an abelian multiplicative finite group of order 4.
SECTION – C
ANSWER ANY TWO QUESTIONS:
19. (a) Find the Fourier series to represent
in the interval
(b) Define Half Range Fourier Series.
20. Solve
(20)
21. (a) Change the order of integration in the integral
(b) Solve
(2 x 20 = 40)
.
(16+4)
.
and evaluate it.
(15+5)
22. (a) Verify Gauss Divergence theorem for
over the
surface of the cube bounded by co-ordinate planes and the plane
.
(b) Prove that the Cancellation law holds good in a Group.
************
(15+5)